The Sun As a Star

The Sun is not only the largest object in our solar
system -- it is also the nearest example of a star.
It produces energy by converting hydrogen to helium, thereby
maintaining a nearly-constant internal temperature. Particles
emitted by the Sun and detected on Earth confirm the details of this
picture.

Topics

Inside the Sun

The Sun's Core

Stability of the Sun

Solar Neutrinos

Reading

&nbsp

12.2

Where Stars Get Their Energy

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p. 282

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Figure it Out 12.1: Energy Generation in the Sun

&nbsp

p. 283

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12.3

Atoms and Nuclei

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p. 283

&nbsp

12.3a

Subatomic Particles

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p. 283-284

&nbsp

12.3b

Isotopes

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p. 284

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12.3c

Radioactivity and Neutrinos

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p. 284-285

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12.4

Stars Shining Brightly

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p. 285-286

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12.5

Why Stars Shine

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p. 286-287

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12.7

The Solar Neutrino Experiment

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p. 288

&nbsp

12.7a

Initial Measurements

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p. 288-289

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12.7b

The Sudbury Neutrino Observatory

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p. 289-290

Inside the Sun

The Sun's interior is made up of the same mix of hydrogen and
helium as its surface. Below the surface layers, three main
regions can be defined. These are the core,
where energy is produced, a radiative zone,
where this energy travels as radiation, and a convective
zone, where energy travels by convection.

Composition of the Sun

The Convective Zone

The convective zone extends from 70% of the Sun's radius
outward to the `surface' or photosphere. While temperatures
in this zone can be very high (millions of degrees), atoms are
still able to keep some of their electrons. As a result, the
gas is opaque to photons (particles of light energy), and
energy is transported outward by the familiar process of
convection. This convective motion ultimately
accounts for most manifestations of solar activity, including
sunspots and the Sun's magnetic field.

The Radiative Zone

The radiative zone extends from 20% to 70% of the Sun's
radius. In this zone, temperatures are high enough to detach
electrons from atomic nuclei, and the gas is said to be
ionized. As a result, photons are able to
diffuse from the core out toward the surface. This is a slow
process -- it takes hundreds of thousands of years for energy
to make its way across the radiative zone. Nonetheless, this
process is efficient enough that convection is not needed to
transport the energy.

Our basic picture of the Sun's interior was
developed by applying the laws of pressure balance and energy
transport to a sphere of hydrogen and helium of known size, mass,
and energy output. But recently, a powerful test has become
possible...

Helioseismology

To study the Sun's structure, we can use the basically the
same method we used earlier for the Earth: monitor
vibrations inside the Sun and use the results to check our
theories.

The Sun is like a big echo chamber, and sound waves
created by turbulence reverberate through its interior.
This diagram shows one possible pattern of vibration in the
Sun. Notice that the wavelength increases going deeper into
the Sun; this implies that the sound speed is increasing.

Doppler Shift

To detect solar vibrations, we use the
Doppler shift of a spectral line of known wavelength.

This diagram shows the Doppler shift for a source of light waves
moving upward. The wavelength is shorter above the source,
and lower below. The faster the source moves, the greater the
difference in wavelength:

λ - λ0 =

v

c

λ0

where c = 3×1010m ⁄ sec
is the speed of light, and v is the speed of the
source.

Doppler Shift

To detect solar vibrations, we use the
Doppler shift of a spectral line of known wavelength.

This diagram shows the Doppler shift for a source of light waves
moving upward. The wavelength is shorter above the source,
and lower below. The faster the source moves, the greater the
difference in wavelength:

λ - λ0 =

v

c

λ0

where c = 3×1010m ⁄ sec
is the speed of light, and v is the speed of the
source.

Solar vibrations cause the surface layers of the Sun
to move up and down with speeds of about
500 m ⁄ sec and periods of about
5 min. Sensitive instruments can detect the shift in
wavelength due to this motion and map it across the face of the
Sun.

Helioseismology Results

One key result of helioseismology is shown in this plot, which
compares the predicted and observed speed of sound at
different depths in the Sun. Perfect agreement would be
represented by a horizontal line. The variations from perfect
agreement are tiny -- less than 0.4% everywhere within
the Sun!

The Sun's Core

Within the Sun's core, the enormous weight of the
overlying material compresses the gas to an almost unimaginable
degree. The density of the gas is roughly

ρ = 150 gm ⁄ cm3 ,

or about 150 times the density of water. The
temperature is about

T = 1.5×107K .

Under such extreme conditions, the hydrogen in the
core of the Sun is slowly transmuted into helium. One by-product is
4.6 billion years of sunshine, with much more to come.

A Pint of the Sun

Descriptions of nuclear `burning' in stars sometimes give the
impression that the central furnace of a star is a place of violent
activity. In fact, the inside of a star is rather peaceful, and
hydrogen burning goes on very slowly.

To appreciate this, imagine we had a magic transporter which could
beam one pint of gas from the center of the Sun right into this room.
One pint of water weighs one pound, but the center of the Sun has a
density about 150 times the density of water, so a pint of sun-stuff
weighs almost as much as I do.

Now the first thing that would happen is that this building would
vanish in a huge explosion. When it was down these in the center of
the Sun, the gas was compressed by the vast weight of all the thick
layers of dense material above it, so it was under enormous pressure.
When it's suddenly transported to Earth, the confining pressure is
removed, and the gas expands -- very rapidly. The explosion would
have the force of a small nuclear bomb.

So if we want to get this experiment approved by the University
administration, we need to make a container which can hold our pint of
sun-stuff under pressure without bursting apart. That's not easy to
do, but we've already assumed we have a transporter right out of Star
Trek, so a little more magic won't be noticed. But our troubles are
not over, because this gas from the center of the sun is incredibly
hot, and the heat would escape in the form of X-rays, cooking everyone
in the vicinity.

OK, let's assume we can make the walls of our container perfectly
reflective, so that all the escaping heat energy is reflected right
back in. I said we were using magic, didn't I? So we have a pint of
sun-stuff sitting right there in front of us, safe as can be. Now
let's allow a little energy to escape -- just exactly the amount of
energy being generated by nuclear reactions, so the gas stays at a
constant temperature. We can use the escaping energy to run a
generator and produce electricity. Thermonuclear power!

But before we call a press conference or make any big deals with
HECO, we better figure out how much energy those bottled nuclear
reactions are generating. And the answer is...

About a thousand times less energy than I'm generating by
breathing. That's all! Per unit mass, the Sun produces much
less energy than a living human body. In total, the Sun generates a
lot of energy, but that's only because it's so massive. If I was as
massive as Jupiter -- perish the thought -- I'd produce more energy
than the Sun, just from my body heat.

Of course, the Sun produces energy by nuclear reactions, while I
produce energy by chemical reactions. That's how the Sun can go on
shining for ten billion years, whereas I get hungry every few
hours.

The enormous lifetime of the Sun gives us another perspective on
the same basic point, which is that nuclear reactions in stars are,
for the most part, very slow and gentle. It takes about ten billion
years for all the hydrogen in the center of the Sun to be burned to
helium. That means that per year, a hydrogen nucleus has about one
chance in ten billion of being involved in a nuclear reaction. The
center of the Sun is an incredibly safe place for hydrogen nuclei! A
hydrogen nucleus in the Sun runs much less risk of undergoing a
nuclear reaction than I do of being hit by lightning.

Energy From Matter

From a physicist's point of view, matter is frozen
energy, and under the right conditions each can be converted to the
other. The conversion of mass m to energy E is
expressed by Einstein's famous equation:

E = mc 2 .

In most people's minds, this equation is associated
with nuclear energy, but in fact it applies to any form of
energy release.

Form of Energy

Example

Efficiency

Chemical Energy

H2 + O → H2O

∼10-8

Nuclear Energy

4p → He4

0.007

Gravitational Energy

mass → black hole

0.1 - 0.3

Isotopes of Hydrogen and Helium

The chemical properties of an element are determined
by the number of electrons orbiting each nucleus -- and since each
electron is balanced by a proton within the nucleus, it's also true
that the chemical properties are determined by the number of protons
in each nucleus. For example, the nucleus of an iron atom has
exactly 26 protons.

However, most elements exist in several forms which
are distinguished by the number of neutrons also present in the
nucleus. These different forms are called isotopes.

Hydrogen and helium have several different isotopes.
Hydrogen (1 proton) can have zero, one, or two neutrons. Helium (2
protons) can have one or two neutrons.

The Proton-Proton Chain

In the Sun's core, nuclei of hydrogen atoms (protons) are
converted to nuclei of helium atoms:

Two protons (p) fuse, forming one deuteron
(d)

This step is very slow, because one p must
change into a neutron (n). A neutrino (ν)
and a positron are produced.

Cosmic Gall

From Telephone Poles and Other Poems, by John Updike

Neutrinos: they are very small
They have no charge; they have no mass;
they do not interact at all.
The Earth is just a silly ball
to them, through which they simply pass
like dustmaids down a drafty hall
or photons through a sheet of glass.
They snub the most exquisite gas,
ignore the most substantial wall,
cold shoulder steel and sounding brass,

insult the stallion in his stall,
and, scorning barriers of class,
infiltrate you and me! Like tall
and painless guillotines they fall
down through our heads into the grass.
At night, they enter at Nepal
and pierce the lover and his lass
from underneath the bed. You call
it wonderful; I call it crass.